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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3840.1.c.a 3840.c 15.d $1$ $1.916$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{9}+q^{15}+q^{25}-q^{27}+\cdots\)
3840.1.c.b 3840.c 15.d $1$ $1.916$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(-1\) \(1\) \(0\) \(q-q^{3}+q^{5}+q^{9}-q^{15}+q^{25}-q^{27}+\cdots\)
3840.1.c.c 3840.c 15.d $1$ $1.916$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(1\) \(-1\) \(0\) \(q+q^{3}-q^{5}+q^{9}-q^{15}+q^{25}+q^{27}+\cdots\)
3840.1.c.d 3840.c 15.d $1$ $1.916$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(1\) \(1\) \(0\) \(q+q^{3}+q^{5}+q^{9}+q^{15}+q^{25}+q^{27}+\cdots\)
3840.1.c.e 3840.c 15.d $2$ $1.916$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{30}) \) \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-iq^{5}+iq^{7}+q^{9}+iq^{15}+\cdots\)
3840.1.c.f 3840.c 15.d $2$ $1.916$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}-q^{15}-q^{23}+\cdots\)
3840.1.c.g 3840.c 15.d $2$ $1.916$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{5}-q^{9}+q^{15}+q^{23}+\cdots\)
3840.1.c.h 3840.c 15.d $2$ $1.916$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{30}) \) \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-iq^{5}-iq^{7}+q^{9}-iq^{15}+\cdots\)
3840.1.i.a 3840.i 120.i $4$ $1.916$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{8}q^{3}-q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
3840.1.i.b 3840.i 120.i $4$ $1.916$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}q^{3}+q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
3840.1.bj.a 3840.bj 60.l $4$ $1.916$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{3}-\zeta_{8}q^{5}+(-1+\zeta_{8}^{2})q^{7}+\cdots\)
3840.1.bj.b 3840.bj 60.l $4$ $1.916$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{3}q^{5}+(-1+\zeta_{8}^{2})q^{7}+\cdots\)
3840.1.bj.c 3840.bj 60.l $4$ $1.916$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots\)
3840.1.bj.d 3840.bj 60.l $4$ $1.916$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{3}+\zeta_{8}q^{5}+(1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
3840.1.bu.a 3840.bu 480.au $8$ $1.916$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{3}+\zeta_{16}^{3}q^{5}+\zeta_{16}^{2}q^{9}-\zeta_{16}^{4}q^{15}+\cdots\)
3840.1.bu.b 3840.bu 480.au $8$ $1.916$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}q^{3}+\zeta_{16}^{3}q^{5}+\zeta_{16}^{2}q^{9}+\zeta_{16}^{4}q^{15}+\cdots\)
3840.1.cl.a 3840.cl 960.bl $16$ $1.916$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{3}q^{3}+\zeta_{32}q^{5}+\zeta_{32}^{6}q^{9}-\zeta_{32}^{4}q^{15}+\cdots\)
3840.1.dy.a 3840.dy 3840.cy $64$ $1.916$ \(\Q(\zeta_{128})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{128}^{29}q^{2}-\zeta_{128}q^{3}+\zeta_{128}^{58}q^{4}+\cdots\)
3840.2.a.a 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
3840.2.a.b 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3840.2.a.c 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3840.2.a.d 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots\)
3840.2.a.e 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+6q^{13}+q^{15}+2q^{19}+\cdots\)
3840.2.a.f 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3840.2.a.g 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}+6q^{13}+\cdots\)
3840.2.a.h 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3840.2.a.i 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}+6q^{11}-6q^{13}+\cdots\)
3840.2.a.j 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-6q^{13}-q^{15}+2q^{19}+\cdots\)
3840.2.a.k 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3840.2.a.l 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3840.2.a.m 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-q^{15}+\cdots\)
3840.2.a.n 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(-1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3840.2.a.o 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}+6q^{13}+\cdots\)
3840.2.a.p 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3840.2.a.q 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+6q^{13}-q^{15}-2q^{19}+\cdots\)
3840.2.a.r 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
3840.2.a.s 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
3840.2.a.t 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
3840.2.a.u 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(-1\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
3840.2.a.v 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3840.2.a.w 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+q^{15}+\cdots\)
3840.2.a.x 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3840.2.a.y 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3840.2.a.z 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-6q^{13}+q^{15}-2q^{19}+\cdots\)
3840.2.a.ba 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots\)
3840.2.a.bb 3840.a 1.a $1$ $30.663$ \(\Q\) None None \(0\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
3840.2.a.bc 3840.a 1.a $2$ $30.663$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
3840.2.a.bd 3840.a 1.a $2$ $30.663$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
3840.2.a.be 3840.a 1.a $2$ $30.663$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
3840.2.a.bf 3840.a 1.a $2$ $30.663$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
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